so the tec3's are fine, but you have limitations. You can't run the inflator hose out the bottom like the razor guys do, you can't run the SPG's up like many Florida divers, and you don't have a rotating turret or ports on the top so it's slightly less ideal. That said I don't think the tec3's are actually good for anything except stages, the DST is much better for doubles, but that's neither here nor there. For sidemount coming from backmount, you NEED to get a longer secondary hose, especially with the Tek3's, a pair of HP hoses, extra SPG and that's it. Your long hose and inflator hoses are perfectly suitable, though maybe less than ideal. Total cost new is $100 for that. The single tank is due to lack of drysuit, but you can always orally inflate the wing, and since you'd only be using AL80's for single tank sidemount, if you're in a drysuit, you don't need to use a wing.
Regarding the canister light, the standard cord lengths are perfectly fine and many divers depending on the rig will actually have them on their hip just like in backmount. Depending on the rig you can also mount them across your back, or up the spine, tons of options. Again, is it ideal? Of course not, the only light that is truly brilliant for sidemount is the UWLD with the side gland, but that doesn't mean anything can't be made to work. Like Victor said, extending the cord is as simple as going to Home Depot and buying some SJOOW cord, which is exactly what is used, making 4 solder connections, and putting the gland back on. That simple, takes 10 minutes if you're a slow solderer.
stage kits as mentioned aren't needed, but if you're a DIR diver, you know how cheap they are to make. Again, go to Home Depot, get some electrical tape, some SS worm gears, some braided line, and you should have extra bolt snaps. If you don't, buying bolt snaps and some gold line is super cheap. Total cost of about $15/tank if you have to buy everything
Plugs for your manifold, no getting around that. $35
Training, not required, though not frowned upon. Depending on where you are located, if you can get to a demo center it may be worth it to help narrow down the rig you ultimately buy as well as remove some frustration. 2 day class at Cave Adventurers is $400
Total cost for that is call it $600 for easy math, plus the rig of your choice. Is it cheap? No, but the training isn't required if you have a buddy who is good at sidemount and can help you get your gear setup, so $200+rig assuming you have to buy a new SPG, hose clamps, and bolt snaps.
Rational reasoning for making the switch? Bedding planes become easier, less risk of cave ceiling damage from the tanks, as you get older being able to carry single tanks, having visual access to your gas supply. Many reasons. I believe in a cave it is a superior and far safer equipment configuration. In open water, I still prefer backmount, but that is personal preference and because I don't have a thick piece of rock over my head, even if there is a decompression obligation, a gas failure on backgas is very different than in a cave. I never made the switch for cave, I did all of my training in sidemount, but I was also doing it before it went mainstream and before gopros so I struggled for many many dives to figure out my equipment configuration because the only instructors were in Florida and I was in college at the time. If you like backmount and are doing mostly open water diving, and are happy, I don't see any reason to make the change other than "because I want to". If you are cave diving, I truly believe it is a better and safer equipment configuration and on that I would recommend that you consider switching. For $1100 you can buy a brand new rig and a full sidemount regulator set vs. $700 for the rig alone